Coefficient of x in `(x + 11) (3-5 x)` is ____

Options

A. 33
B. `-5`
C. 3
D. `-52`

Answer

To find the coefficient of \( x \) in the expression \( (x + 11)(3 - 5x) \), we will follow these steps:

### Step 1: Expand the expression
We will use the distributive property (also known as the FOIL method for binomials) to expand the expression.

\[ (x + 11)(3 - 5x) = x \cdot 3 + x \cdot (-5x) + 11 \cdot 3 + 11 \cdot (-5x) \]

### Step 2: Calculate each term
Now we calculate each of the terms:

1. \( x \cdot 3 = 3x \)
2. \( x \cdot (-5x) = -5x^2 \)
3. \( 11 \cdot 3 = 33 \)
4. \( 11 \cdot (-5x) = -55x \)

### Step 3: Combine like terms
Now we combine all the terms we calculated:

\[ 3x - 5x^2 + 33 - 55x \]

Combining the \( x \) terms:

\[ 3x - 55x = -52x \]

So, the expression simplifies to:

\[ -5x^2 - 52x + 33 \]

### Step 4: Identify the coefficient of \( x \)
The coefficient of \( x \) in the expression \( -5x^2 - 52x + 33 \) is the number in front of \( x \), which is \( -52 \).

Thus, the coefficient of \( x \) is:

\[ \text{Coefficient of } x = -52 \]

### Final Answer:
The coefficient of \( x \) in the expression \( (x + 11)(3 - 5x) \) is \( -52 \).

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